The center of a hyperbola is (-2,4), and one vertex is (-2,7). The slope of one of the asymptotes is 1/2.

What is the equation of the hyperbola in standard form?

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The equation of the hyperbola in standard form is (y^2 / 49) - (x^2 / 4) = 1.

Step-by-step explanation:

Hyperbola is a section of the cone formed by intersecting a right circular cone with a plane at an angle where both halves of the cone are intersected. The vertex and the center of the hyperbola are present both on the same line x = - 2. (i. e. on the y-axis), hence the branches of the hyperbola are above and below each other. The slope of the asymptotes is + (or) - a/b.

Here the vertex is 7 units so a = 7 and a^2 = 49.

Slope of the asymptotes = a/b = 1/2.

Here b = 2 and b^2 = 4.

The standard equation of the hyperbola is,

(y^2 / 49) - (x^2 / 4) = 1.